02-01-2013, 12:48 PM
SELECTING AN APPROPRIATE FILTER
1SELECTING AN APPROPRIATE FILTER.pptx (Size: 78.47 KB / Downloads: 29)
We have five approaches to remove noise and interference:
(1) synchronized or ensemble averaging of multiple realizations or copies of a signal -time domain,
(2) MA filtering-time domain,
(3) frequency-domain filtering-spectrum,
(4) optimal (Wiener) filtering-time and frequency domain,
(5) adaptive filtering-time domain.
Synchronized or ensemble averaging is possible when:
The signal is statistically stationary, (quasi)periodic, or cyclo-stationary.
Multiple realizations or copies of the signal of interest are available.
A trigger point or time marker is available, or can be derived to extract and align the copies of the signal.
The noise is a stationary random process that is uncorrelated with the signal and has a zero mean (or a known mean).
Temporal MA filtering is suitable when:
The signal is statistically stationary at least over the duration of the moving window.
The noise is a zero-mean random process that is stationary at least over the duration of the moving window and is independent of the signal.
The signal is a relatively slow (low-frequency) phenomenon.
Fast, on-line, real-time filtering is desired.
Frequency-domain fixed filtering is applicable when:
The signal is statistically stationary.
The noise is a stationary random process that is statistically independent of the signal.
The signal spectrum is limited in bandwidth compared to that of the noise (or vice-versa).
Loss of information in the spectral band removed by the filter does not seriously affect the signal.
On-line, real-time filtering is not required (if implemented in the spectral domain via the Fourier transform).
The optimal Wiener filter can be designed if
The signal is statistically stationary.
The noise is a stationary random process that is statistically independent of the signal.
Specific details (or models) are available regarding the ACFs or the PSDs of the signal and noise.
Adaptive filtering is called for and possible when:
The noise or interference is not stationary and not necessarily arandom process.
The noise is uncorrelated with the signal.
No information is available about the spectral characteristics of the signal and noise, which may also overlap significantly.
A second source or recording site is available to obtain a reference signal that is strongly correlated with the noise but uncorrelated with the signal.